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gptkbp:instanceOf
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gptkb:group_of_people
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gptkbp:abbreviation
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gptkb:MCG
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gptkbp:actsOn
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gptkb:Teichmüller_space
fundamental group of surface
homology of surface
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gptkbp:defines
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the group of isotopy classes of orientation-preserving self-homeomorphisms of a surface
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gptkbp:field
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gptkb:topology
geometric group theory
low-dimensional topology
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gptkbp:hasProperty
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finitely presented
generated by Dehn twists
linear for genus 1
not linear for genus > 1
residually finite
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gptkbp:notation
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Mod(S)
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gptkbp:relatedTo
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gptkb:Heegaard_splitting
gptkb:Dehn_twist
gptkb:Gromov_boundary
gptkb:Johnson_homomorphism
gptkb:Nielsen–Thurston_classification
gptkb:Torelli_group
gptkb:pseudo-Anosov_map
gptkb:hyperbolic_geometry
gptkb:Artin_group
gptkb:moduli_space_of_Riemann_surfaces
gptkb:modular_functor
representation theory
modular group
orthogonal group
braid group
3-manifold
monodromy
quantum invariants
pants decomposition
Out(F_n)
automorphism group of free group
curve complex
curve graph
surface bundle
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gptkbp:studiedBy
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gptkb:John_H._Conway
gptkb:Dennis_Johnson
gptkb:Curtis_McMullen
gptkb:Joan_Birman
gptkb:William_Thurston
gptkb:Benson_Farb
gptkb:Dan_Margalit
gptkb:Nikolai_Ivanov
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gptkbp:bfsParent
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gptkb:Topology
gptkb:Group_theory
gptkb:Riemannian_manifold
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gptkbp:bfsLayer
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5
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